Will EEVEE eliminate the need for cycles and rendering?
No. EEVEE will not replace cycles.

If you want accurate renders, cycles will still be your renderer. Cycles is a ray tracer, so it simulates individual rays of light your scene.

EEVEE uses approximations on the behavior of light and will not be as accurate, however is much faster.

For some projects (such as low-poly renders or stylized works), EEVEE could replace cycles, but when it comes to photorealism, cycles will still be the champion.